We derive a general formula for the time decay, theta, for out-of-the-money European options on stocks and bonds at expiry, in terms of the density of jumps and payoff. Explicit formulas are derived for the standard put and call options, exchange options in stochastic volatility and local...

New methods for solving general linear parabolic partial differential equations (PDEs) in one space dimension are developed. The methods combine quadratic-spline collocation for the space discretization and classical finite differences, such as Crank-Nicolson, for the time discretization. The...

A general numerical method for pricing American options in regime switching jump diffusion models of stock dynamics with stochastic interest rates and/or volatility is developed. Time derivative and infinitesimal generator of the process for factors that determine the dynamics of the interest...

With the evolution of Graphics Processing Units (GPUs) into powerful and cost-efficient computing architectures, their range of application has expanded tremendously, especially in the area of computational finance. Current research in the area, however, is limited in terms of options priced and...

This paper suggests a new method of implementing the principle of maximum entropy to retrieve the risk neutral density of future stock, or any other asset, returns from European call and put prices. Instead of options prices used by previous studies, the method maximizes the entropy measure...

Breakthroughs and backlashes have marked progress in the development and diffusion of Artificial Intelligence (AI). These shocks make the investment in developing an Artificial General Intelligence (AGI) subject to considerable uncertainty. This paper applies a real options model, extended to...

This paper solves the dynamic investment problem of a risk averse agent compensated with a performance related bonus plus a salary guaranteed up to a certain level of underperformance. The main contribution is to explicitly take into account the financial fragility of the principal [employer],...

We find the variance-optimal equivalent martingale measure when multivariate assets are modeled by a regime-switching geometric Brownian motion, and the regimes are represented by a homogeneous continuous time Markov chain. Under this new measure, the Markov chain driving the regimes is no...

This paper analyses the implementation and calibration of the Heston Stochastic Volatility Model. We first explain how characteristic functions can be used to estimate option prices. Then we consider the implementation of the Heston model, showing that relatively simple solutions can lead to...